Bootstrapping the Kaplan-Meier Estimator on the Whole Line

TL;DR

This paper proves the consistency of Efron's bootstrap for the Kaplan-Meier estimator across the entire support, enabling simultaneous confidence bands and practical applications in survival analysis.

Contribution

It establishes the bootstrap's consistency on the whole support, allowing for new confidence bands and inference methods in survival analysis.

Findings

Bootstrap is consistent for the entire survival function

Enables construction of simultaneous confidence bands

Supports practical applications like Gini index confidence intervals

Abstract

This article is concerned with proving the consistency of Efron's (1981) bootstrap for the Kaplan-Meier estimator on the whole support of a survival function. While other works address the asymptotic Gaussianity of the estimator itself without restricting time (e.g. Gill, 1983, and Ying, 1989), we enable the construction of bootstrap-based time-simultaneous confidence bands for the whole survival function. Other practical applications include bootstrap-based confidence bands for the mean residual life-time function or the Lorenz curve as well as confidence intervals for the Gini index.